Alternative factors that account for a limitation of the period of injection of picosecond runaway electron bunches in air-filled diode with inhomogeneous electric field are analyzed. Experimental data on the characteristics of such electron beams have been obtained under the conditions with variable emissive properties of the cathode, time of the voltage prepulse action, and electric field strength in the region of electron injection. Based on these data, a hypothesis is formulated and justified that the mechanism of limitation related to a transition from the field electron emission to the explosion of microinhomogeneities is less probable than the mechanism of current limitation by a screening plasma cloud formed over the point electron emitters.